The polynomial mapping method and its applications analysis  Page description

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Details of project

 
Identifier
44782
Type NI
Principal investigator Totik, Vilmos
Title in Hungarian A polinomális-leképezés módszer és annak alkalmazásai az analízisban
Title in English The polynomial mapping method and its applications analysis
Panel Natural Sciences large proposals
Department or equivalent Bolyai Institute (University of Szeged)
Participants Benko, Dávid
Fekete, Árpád
Krámli, András
Leindler, László
Móricz, Ferenc
Nagy, Béla
Németh, József
Németh, Zoltán
Nikolényi, István
Simányi, Nándor
Szalay, István
Tandori, Károly
Toókos, Ferenc
Starting date 2003-01-01
Closing date 2005-12-31
Funding (in million HUF) 55.200
FTE (full time equivalent) 0.00
state closed project





 

Final report

 
Results in Hungarian
A pályázat által támogatott kutatások a komplex függvénytanhoz, a sorelmélethez és a potenciálelmélethez kapcsolódnak. Pályázati támogatással egy könyv, 37 tudományos közlemény és 4 doktori disszertáció született. A főbb kutatási területek a következők voltak: - harmonikus mértékek és Green függvények becslése végtelenszer összefüggő tartományokon - a polinom-inverz kép módszer és polinom-egyenlőtlenségek - a polinom-inverz kép módszer és polinom-approximáció - Green függvények Hölder folytonossága - ortogonális polinomok - beágyzási tételek - sorelmélet - statisztikus konvergencia - Fourier-sorok - approximációelmélet Ezen kérdésekkel kapcsolatos kutatásaink és publikációink jelentős mértékben gazdagítottak e területekre vonatkozó ismereteinket.
Results in English
The research supported by the project is connected with function theory, the theory of series and potential theory. One book, 37 scientific publications and 4 PhD dissertations were published with the support of the project. The major areas were the following: - harmonic measures and Green's functions on infinitely connected domains - the polynomial-inverse image method and polynomial inequalities - the polynomial-inverse image method and polynomial approximation - Holder continuity of Green's functions - orgthogonal polynomials - imbedding theorems - statistical convergence - Fourier series - approximation theory The supported research and publications in connection with these questions considerably enhanced our understanding of these areas.
Full text http://real.mtak.hu/1240/
Decision
Yes





 

List of publications

 
J. Németh: Embedding relations and generalized Lipschitz-classes, Acta Sci. Math., 2005
V. Totik: Orthogonal polynomials, Surveys in Approximation Theory, 2005
P. Varjú: Approximation by homogeneous polynomials, Constr. Approx., 2006
B. Nagy and V. Totik: Sharpening of Hilbert's theorem, J. Anal. Math., 2005
V. Totik Equilibrium measures and polynomials: Equilibrium measures and polynomials, Prooceedings of the 4th European Congress of Mathematics Stockholm, J. Anal. Math., 2005
J. Németh: A remark on the degree of approximation of continuous functions, Acta Math. Hungar, 2005
B. Simon and V. Totik: Limits of zeros of orthogonal polynomials on the circle, Mathematische Nachrichten, 2005
I. Szalay: Explision and compressin by numbers, International Journal of Applied Mathematics, 2005
F. Móricz: Regular statistical convergence of Double sequences, Colloquium Mathematicum, 2005
F. Móricz: Regular statistical convergence of multiple sequences, Analysis Math., 2005
L. Golinskii and V. Totik: Orthogonal polynomials from Jacobi to Simon, AMS kiadvány, 2005
L. Leindler: Embedding results regarding strong approximation of sine series, Acta Sci. Math., 2005
L. Leindler: Embedding results regarding strong approximation of Fourier series. IV., Analysis Mathematica, 2005
L. Carleson and V. Totik: Hölder continuity of Green's functions, Acta Sci. Math, 2004
L. Baratchart, R. Küstner and V. Totik: Zero distribution via orthogonality, Annales de l'Institut Fourier, 2005
D. Benkő: The support of the equilibrium measure, Acta Sci. Math., 2004
F. Toókos: A wiener-type condition for Hölder continuity, Acta Math. Hungarica, 2005
F. Toókos and V. Totik: Markov inequality and Green functions, Rend. Circ. Mat. Palermo, 2005
L. Leindler: Embedding results pertaining to strong approximation of Fourier series. V., Anal. Math., 2007
L. Leindler: On the relationships of seven numerical sequences, Acta Math. Hung., 2007
L. Leindler: A newer class of numerical sequences and its applications to sine and cosine series, Anal. Math., 2007
L. Leindler: A new extension of monotone sequences and its applications, Journal of Inequalities in Pure and Applied Mathematics, 2006
L. Leindler: A note on the best approximation of sine and cosine series, Analysis Math., 2006
L. Leindler: On embedding of the class H^\omega, Journal of Inequalities in Pure and Applied Mathematics, 2004
L. Leindler: A recent note on the absolute Riesz summability factors, Journal of Inequalities in Pure and Applied Mathematics, 2006
L. Leindler: Integrability of sine and cosine series having coefficients of a new class, Australian Journal of Mathematical Analysis and Applications, 2004
L. Leindler: A note on the absolute Riesz summability factors, Journal of Inequalities in Pure and Applied Mathematics, 2005
F. Móricz: The classical monotone convergence theorem of Beppo Levi fails in noncommutative L_2-spaces, Proceedings of the American Mathematical Society, 2005
F. Móricz: Valós és komplex számok végtelen szorzatai, Polygon, 2005
F. Móricz: Tauberian conditions for double sequences that are statistically summable by weighted means, Sarajevo Journal of Mathematics, 2005
F. Móricz: Strong Cesáro summability and statistical limit of double Fourier integrals, Acta Sci. Math., 2005
G. Brown, D. Feng and F. Móricz: The maximal conjugate and Hilbert operators on real Hardy spaces, Acta Math. Hungar., 2005
F. Móricz: Multivariate Hausdorff operators on the spaces H^1 (R^n) and BMO(R^n), Analysis Mathematica, 2005
B. Nagy: Asymptotic Bernstein inequality on lemniscates, J. Math. Anal. Appl., 2005
B. Nagy: Higher order shrpness of the generalized Hilbert's lemmiscate theorem, Approximation theory XI, Mod. Methods Math., 2005
F. Toókos: Smoothness of Green's functions and density of sets, Acta Sci. Math., 2005
P. Nevai and V. Totik: Denisov's theorem on recurrence coefficients, J. Approx. Theory, 2004
Toókos Ferenc: Green függvények simasága, SZTE, 2005
V. Totik: Metric Properties of Harmonic Measures, Memoirs of the American Mathematical Society, 2006
Nagy Béla: Aszimptotikus Bernstein-típusú egyenlőtlenségek, SZTE, 2006
Benkő Dávid: Az egyensúlyi mérték és Saff sejtése, SZTE, 2006
Fekete Árpád: Statisztikus konvergencia, SZTE, 2006




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